7.3. Problems 51
7.4. Answers to Odd-Numbered Exercises 53
Chapter 8. BASIS FOR A VECTOR SPACE 55
8.1. Background 55
8.2. Exercises 56
8.3. Problems 57
8.4. Answers to Odd-Numbered Exercises 58
Part 3. LINEAR MAPS BETWEEN VECTOR SPACES 59
Chapter 9. LINEARITY 61
9.1. Background 61
9.2. Exercises 63
9.3. Problems 67
9.4. Answers to Odd-Numbered Exercises 70
Chapter 10. LINEAR MAPS BETWEEN EUCLIDEAN SPACES 71
10.1. Background 71
10.2. Exercises 72
10.3. Problems 74
10.4. Answers to Odd-Numbered Exercises 75
Chapter 11. PROJECTION OPERATORS 77
11.1. Background 77
11.2. Exercises 78
11.3. Problems 79
11.4. Answers to Odd-Numbered Exercises 80
Part 4. SPECTRAL THEORY OF VECTOR SPACES 81
Chapter 12. EIGENVALUES AND EIGENVECTORS 83
12.1. Background 83
12.2. Exercises 84
12.3. Problems 85
12.4. Answers to Odd-Numbered Exercises 86
Chapter 13. DIAGONALIZATION OF MATRICES 87
13.1. Background 87
13.2. Exercises 89
13.3. Problems 91
13.4. Answers to Odd-Numbered Exercises 92
Chapter 14. SPECTRAL THEOREM FOR VECTOR SPACES 93
14.1. Background 93
14.2. Exercises 94
14.3. Answers to Odd-Numbered Exercises 96
Chapter 15. SOME APPLICATIONS OF THE SPECTRAL THEOREM 97
15.1. Background 97
15.2. Exercises 98
15.3. Problems 102
15.4. Answers to Odd-Numbered Exercises 103
Chapter 16. EVERY OPERATOR IS DIAGONALIZABLE PLUS NILPOTENT 105
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